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A Linear equation in point slope form using the first point 3/4h , 9 in that can be used to determine the level of chocolate syrup in dispenser after x hours is y = -4x + 12 .

In the question ,

it is given that

in 3/4 hours the the level of chocolate syrup was 9 inch ,

So , the first point is (3/4,9) .

in 5/4 hours the level of chocolate syrup in the dispenser was 7 inch .

So , the second point is (5/4,7)

to find the linear equation we first need to find the slope .

Slope = (7-9)/(5/4-3/4)

= -2/(2/4)

= -4

So , the equation in slope intercept form having point (3/4 , 9) and slope -4 is    .

(y - 9) = -4(x - 3/4)

y - 9 = -4x + 3

y = -4x + 3 + 9

y = -4x + 12

Therefore , The linear equation is y = -4x + 12 .

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A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.

Answer:

ASA

Step-by-step explanation:

1) the angles are congruent where they intercept in blue

2) the sides that are congruent are between the two congrunet  angles  the blue ones and the given ones

Thus the largest length is 15 inches

Size (l) is 14 inches.

Size (w) = 4 inches.

Height is 4 inches (h).

The distance between one bottom corner and the opposite top corner is known as d. Find s, the diagonal across the bottom of the box, first.

[tex]w^2 + l^2 = s^2[/tex]

Replace the prescribed measures.

[tex]4^2 + 14^2 = s^2[/tex]

Simplify.

[tex]16 + 196 = s^2[/tex]

[tex]21^2= s^2[/tex]

To determine d, use the expression for s.

[tex]h^2 + s^2 = d^2[/tex]

Plug in s2 = 212 and h = 4.

4^2 + 21^2 = d^2

Simplify.

16 + 21^2 = d^2

228 = d2

On both sides, take the square root.

√228 = √d2

15.1 ≈ d

Therefore, the part's maximum possible length was 15 inches.

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Answers. 230 is the answer that I got

Answer:   b

Step-by-step explanation:

The 28th percentile for the number of chocolate chips in the bag is 1192.206

To determine the 28th percentile for the number of chocolate chips in the bag, we find the z-score for the 28th percentile.

Found using a z-table or z-calculator, the z-score for the 28th percentile is -0.583

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 28th percentile,

X = 1261 + (-0.583)(118)

X = 1261 - 68.79 = 1192.206

Hence the 28th percentile id 1192.206

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The equation of the line is y=-x-4

How to find whether line is perpendicular or not?

Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

The given line is

y=x-1

the slope of it is 1

As the slopes of perpendicular lines are negative reciprocals

So, the slope of the perpendicular line is -1

As the point is(-6,2)

y=mx+b

y=(-1)x+b

2=-1(-6)+b

2=6+b

b=2-6

b=-4

∴The equation of the line that is perpendicular is  y=-x-4

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Answer:

Step-by-step explanation:

she will pay $80 in interest.

=====================================================

Work Shown:

x = number of nickels

y = number of dimes

5x = value of the nickels only (cents)

10y = value of the dimes only (cents)

5x+10y = total value of all the coins = 75 cents

One equation we can form is 5x+10y = 75.

"he has twice as many dimes as nickels" tells us that y = 2x. We can replace every copy of y with 2x and solve for x as shown in the steps below.

5x+10y = 75

5x+10(y) = 75

5x+10(2x) = 75 ... plug in y = 2x

5x+20x = 75

25x = 75

x = 75/25

x = 3

This value leads to y = 2x = 2*3 = 6

Johnny has 3 nickels and 6 dimes.

------------------

Check:

1 nickel = 5 cents

3 nickels = 3*5 = 15 cents

1 dime = 10 cents

6 dimes = 6*10 = 60 cents

3 nickels + 6 dimes = 15 cents + 60 cents = 75 cents = $0.75

The answers are confirmed.

As the sample size (n) increases, the number of degrees of freedom increases, and the t-distribution approaches a normal distribution.

What is degrees of freedom ?

The variety of degrees of freedom is the amount of values within the final calculation of a datum that are liberal to vary. Estimates of applied math parameters are often primarily based upon totally different amounts information|of knowledge or data.

Main Body:

Degrees of freedom typically equals the quantity of observations (or items of information) minus the quantity of parameters calculable. once you perform regression, a parameter is calculable for each term within the model, and and every one consumes a degree of freedom. Therefore, as well as excessive terms during a multivariate analysis model reduces the degrees of freedom on the market to estimate the parameters' variability.

Hence the number of degrees of freedom increases,as the sample size (n) increases.

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The polynomial function with third degree, zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)

Polynomial function:

polynomial function means a functions of single independent variables, in which variables can occur more than once, raised to an integer power.

Given,

Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.

And we need to construct  a polynomial function with the stated properties and reduce all fractions to lowest terms.

We know that the standard form for the third degree polynomial function is written as,

=> y = K (x + zeros1) (x + zeros2) (x + zeros3)

The third degree, zeros of the function is -3, -1 and -4.

Now, we have to apply it on the general form,

=> y = K (x -3) (x - 1) (x + 4) ----------------------(1)

Here we know the value of y intercept is -13 then the value of x is 0.

So, it can be written as,

=> -13 = K(0 - 3) (0 - 1) (0 + 4)

=> -13 = K (12)

Therefore, the value of K = -13/12

Now, apply the values on the equation (1), then we get,

=> y = -13/12 (x -3) (x - 1) (x + 4)

Therefore, the third degree polynomial function is,

=> y = -13/12 (x³ - 13x + 12)

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The product of the radical expression is  - 49 + 13√7. option B is the correct answer

From the question, we have

(7-√7)(-6+√7)

= (7) × (-6) + (-√7) × (√7) + (-√7) × (-6) + (7)(√7)

= -42 - 7 + 6√7 + 7√7

= - 49 + 13√7

The product of the radical expression is  - 49 + 13√7

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The relative displacement of the given case is δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

Given;

To get the axial load-related relative displacement of one end of the tapered plate concerning the other end.

Let 'd' be the displacement;

We know,

[tex]w = d1 + \frac{(d2-d1)x}{h} = \frac{d1h+(d2-d1)x}{h}[/tex]

To calculate the relative displacement;

δ = [tex]\int\limits {\frac{p(x)}{A(x)E} } \, dx =p/E \int\limits {\frac{1}{\frac{d1h+(d2-d1)x}{h}t } } \, dx[/tex]

δ = [tex]ph/Et\int\limits^h_0 {\frac{dx}{d1h+(d2-d1)x} } \,[/tex]

δ = [tex]\frac{ph}{Et(d2-d1)}[ln(1+\frac{d2-d1}{d1}) ][/tex]

δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

Therefore, the Relative displacement of the given case is δ = [tex]\frac{ph}{Et(d2-d1)}ln(\frac{d2}{d1} )[/tex]

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The ordered pair of a solution of the inequality are (10, 0) and (0, 5).

The given inequality is x+2y>10.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Graph the inequality by finding the boundary line, then shading the appropriate area.

The solution of the inequality is (10, 0) and (0, 5).

Hence, the ordered pair of a solution of the inequality are (10, 0) and (0, 5).

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Answer:

Since 1 scoop of ground coffee makes 1 cup of coffee, Andy can make 24 cups of coffee from the jar.

Step-by-step explanation:

Answer:960000000

Step-by-step explanation:

Answer: 960000000

Step-by-step explanation:

960 times 1.0 times 10^6 look it up !!

If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Step-by-step explanation:

n^2 - n -56 = 0

n^2 -8n +7n-56 = 0

n(n-8) +7(n-8) = 0

(n+7)(n-8) = 0

n = (-7,8)

option B

1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

1 + 2 = 3

As we know, from the definition:

Arithmetic can be defined as, an operation in which we do the addition of numbers, subtraction, multiplication, and division.

For the addition of two numbers:

The two numbers are 1 and 2:

Draw a vertical line 1:  |

Draw two vertical lines 2:  | |

Count the lines:  | | | = 3

Thus, 1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

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Answer:
D

Step-by-step explanation: 5 are crossed rows by 3 and then 7 by 5 are shaded in and than is 2 different numbers in together multiplied equals 1.500 which is D

Answer:

1. -3

2. 6

3.less than

Step-by-step explanation:

Answer:

Angles 2, 3, 6, and 7 will be the same with 41 degrees!

Angles 1, 4, 5, and 8 are the same with 139 degrees!

Step-by-step explanation:

Opposite angles are the same so that makes angles 2, 3, 6, and 7 the same at 41 degrees!

The same rule applies to angles 1, 4, 5, and 8 and we have to subtract!

180 - 41 = 139 degrees!

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Answer:

Step-by-step explanation:

Write the value of x when y is = 7

x = 7

x = -1

x = -4

The slope of the line is 3/2, Equation of the line in point-slope form ( y - 10) = 3/2 (x-2), and The equation of the line in slope-intercept form

y = (3/2) x - 13

Using the slope formula, calculate the slope. To find the y-intercept (b), use the slope and one of the points.

Once you know the values for m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to derive the line's equation.

Therefore,

A line goes through the points (2,10) and (-2,4).

Slope = (y2-y1)/(x2 -x1)

= (4 - 10) / (-2 - 2)

= -6/-4 = 3/2

The equation of the line in point-slope form using the point (2,10)

Slope  = 3/2

equation of the line in point slope form :

(y - y1) = m (x -x1)

(y - 10) = 3/2 (x-2)

y = mx + c

Simplifying the above equation, then we get

2 = 3/2 × 10 + c

c = 2 - 15

c = -13

equation of the line is

y = (3/2)x - 13

2y = 3x - 26

the slope-intercept equation of the line

y = (3/2) x - 13

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The point that represent the origin in the number line is Point W

A number line is a horizontal representation of numbers in parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right

number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p

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